The collection of all \(\tau \) -measurable operators is denoted by \(S(\tau )\) .
With the sum and product defined as the respective closures of the algebraic sum and
product, it is well known that \(S(\tau )\)   is a *-algebra. For
\(\epsilon ,\ \delta >0\) , we denote by \(V(\epsilon ,\delta )\)  the set
of all \(x\in S(\tau )\)  for which there exists an orthogonal
projection \(p\in P(\mathcal {M})\)  such that \(p({\mathcal {H}})\subseteq {\mathcal {D}}(x),\ \Vert xp\Vert _{{\mathcal {B}}({\mathcal {H}})}\le \epsilon \)  and \(\tau ({\textbf {1}}-p)\le \delta \) . The sets \(\lbrace V(\epsilon ,\delta ):\epsilon ,\ \delta >0\rbrace \) 
form a base at 0 for a metrizable Hausdorff topology on
\(S(\tau )\) , which is called the measure topology. Equipped
with this topology, \(S(\tau )\)  is a complete topological
\(*\) -algebra. These facts and their proofs can be found in the
papers [1]}, [2]}. See also  [3]}
